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Academic Report ( 2019–20 ) Harish - Chandra Research Institute Chhatnag Road, Jhunsi Prayagraj (Allahabad), India 211019 Contents 1. About the Institute 2 2. Director’s Report 4 3. List of Governing Council Members 5 4. Staff List 7 5. Academic Report - Mathematics 15 6. Academic Report - Physics 100 7. HRI Colloquia 215 8. Mathematics Talks and Seminars 216 9. Physics Talks and Seminars 218 10. Recent Graduates 222 11. Publications 224 12. Preprints 233 13. About the Computer Section 240 14. Library 242 15. Construction Activity 245 1 About The Institute History The Harish-Chandra Research Institute is one of the premier research institutes in the country. It is an autonomous institution fully funded by the Department of Atomic En- ergy (DAE), Government of India. The Institute was founded as the Mehta Research Institute of Mathematics and Mathematical Physics (MRI). On 10th Oct 2000 the In- stitute was renamed as Harish-Chandra Research Institute (HRI) after the acclaimed mathematician, the late Prof Harish-Chandra. MRI started with the efforts of Dr. B. N. Prasad, a mathematician at the University of Allahabad, with initial support from the B. S. Mehta Trust, Kolkata. Dr. Prasad was succeeded in January 1966 by Dr. S. R. Sinha, also of Allahabad University. He was followed by Prof. P. L. Bhatnagar as the first formal Director. After an interim period, in January 1983 Prof. S. S. Shrikhande joined as the next Director of the Institute. During his tenure the dialogue with the DAE entered into decisive stage and a review committee was constituted by the DAE to examine the Institute’s future. In 1985 Shri N. D. Tiwari, the then Chief Minister of Uttar Pradesh, agreed to provide sufficient land for the Institute and the DAE promised financial support for meeting both the recurring and non-recurring expenditure. In January 1990, about 66 acres of land was acquired in Jhunsi, Allahabad, and the Institute came up at this site. Prof. Shrikhande was followed by Prof. H. S. Mani who took over as the Director in January 1992. With his joining, and the shift to the new campus at Jhunsi in 1996, the Institute’s activities picked up pace. After a distinguished tenure of about nine years Prof. Mani retired in August 2001 and the charge was taken over by Prof. R. S. Kulkarni. After Prof. Kulkarni’s tenure, Prof. Amitava Raychaudhuri was the Director from July 19, 2005 to May 15, 2011. After him Prof. Sumathi Rao officiated as Acting Director till April 28, 2012. Prof. Jayanta Kumar Bhattacharjee was the next Director and continued till April 9, 2017. Prof. Pinaki Majumdar, the current Director, took over on April 10, 2017. The Institute has a residential campus in Jhunsi, Allahabad, with a library, state of the art computational facility and fast internet link to the outside world. There is an active Ph.D program, an M.Sc program in Physics that started in 2017, and a large traffic of visiting scientists and students. Research The Institute continues to be devoted to fundamental research in diverse areas of mathematics and theoretical physics. Research is carried out by faculty members, vis- iting scientists, post-doctoral fellows and Ph.D. students. The mathematics group at HRI carries out research in several areas. In algebra, work is done on algebraic groups and related structures, the theory of groups and group rings, representation theory, and infinite-dimensional Lie algebras. Work in analysis is in the field of harmonic analysis of Lie groups. Activity in geometry in- cludes discontinuous groups and Riemann surfaces, algebraic topology, variational problems on manifolds, Chow groups of rational surfaces, and moduli of vector bun- dles. The number theory group works on algebraic, analytic and combinatorial num- ber theory, automorphic forms and cryptography. 2 The areas of research in physics are astrophysics, condensed matter physics, quan- tum information and computing, high energy phenomenology and string theory. In astrophysics, work is done on the cosmic microwave background, large scale structure formation, and galaxy evolution. Main areas of activity in condensed matter physics are strongly correlated systems, mesoscopic systems, and the study of clusters and nanomaterials. In string theory, perturbative and non-perturbative aspects of string theory and quantum field theory are being actively investigated. Research in neutrino physics, strong interactions, lattice gauge theory, supersymmetry and various aspects of physics beyond the standard model is done in high-energy phenomenology. The Institute is a member of the India-based Neutrino Observatory (INO) collaboration. Recognition Since 1992 the Institute has attracted worldwide attention, as is evident from the recog- nition received by many of its members. Several members of the Institute have been recognised for their scientific contribution. Prof. Ashoke Sen, Prof. B. Mukhopad- hyaya, Prof. Pinaki Majumdar and Prof. Rajesh Gopakumar have been awarded the Shanti Swarup Bhatnagar prize and in 2018 Prof. Aditi Sen De became the first woman scientist in India to be awarded the Bhatnagar prize in Physical Sciences. The out- standing contribution of Prof. Ashoke Sen has been recognised by a Fellowship of the Royal Society, the award of Padmashri and Padmabhushan and the award of one of the first Fundamental Physics Prize (2012) from the Yuri Milner Foundation. He was the only recipient of the prize from all of Asia. In 2017 the Institute was recognised as being among the top 10 research centers in India by the Nature journal. 3 Director’s Report March 2020 marked the temporary end of the world as we knew it. As I write, we are still in the grip of the pandemic, with many activities suspended and some moved online. The April 2019 to March 2020 period however was vibrant. I touch upon the activities below. We had the ”AFS-I- Annual Foundation School” in Mathematics in May 2019, and two conferences in the subsequent period. One was a meeting on ”Class groups of number fields and related topics” in Oct 2019. This was the third in a series of meetings being held at HRI. In March 2020 we had a mini workshop on ”Bundles, Cycles, and Motives”. We maintained an active Visitors Program, using the generous support provided by the Infosys Foundation. The Visiting Professors spend a week or more at HRI and deliver a set of lectures on some topic in their field. Over this period, in Mathematics we had V. Kumar Murty from the Field’s Institute, University of Toronto, in October, Joachim Toft, from Linnaeus University, Sweden, and Jean-Marc Deshouillers from Institute of Mathematics of Bordeaux in November, and Kamal Khuri-Makdisi from the American University, Beirut, in January. In Physics we had Jainendra Jain from Penn State in June, John McGrady from Oxford University in September, and Yuval Gefen from Weizmann and Ribhu Kaul from the University of Kentucky, in January. We held our annual Talent Search examination for school level children in Alla- habad, and activities promoting the rajbhasha. The HRI colloquia featured talks by ed- ucationists, historians, economists and of course physicists and mathematicians from across the country. A larger than average number of students graduated during this period. A total of 24 students (10 in Math and 14 in Physics) completed their Ph.D requirements. For the current year the entire admission process in Physics and Mathematics has been moved online. The number of papers published over the period would be around 110. Pinaki Majumdar Director 4 List of Governing Council Members (2019 - 20) 1. Shri K.N. Vyas Chairman, Atomic Energy (Chairman) Commission (AEC) & Secretary, Department of Atomic Energy, Govt. of India, Anushakti Bhawan, Chhatrapati Shivaji Maharaj Marg, Mumbai 400 001 2. Shri A.R. Sule Joint Secretary (R & D) Deptt. of Atomic Energy, Govt. of India, Anushakti Bhavan, Chhatrapati Shivaji Maharaj Marg, Mumbai 400 001 3. Mrs. Richa Bagla Joint Secretary (Finance) Deptt. of Atomic Energy, Govt. of India, Anushakti Bhavan, Chhatrapati Shivaji Maharaj Marg, Mumbai 400 001 4. Prof. V. Srinivas Senior Professor TIFR & Chairman NBHM, School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005 5. Prof. V. Arvind Director Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113 6. Prof. Sanghamitra Bandopadhyay Director Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108 7. Prof. S.M. Chitre Chair, Academic Board University of Mumbai - Department of Atomic Energy - Centre for Excellence in Basic Sciences (UM-DAE-CBS), Health Centre Building, University of Mumbai, Kalina Campus, Mumbai 400 098 5 8. Director, Higher Education Higher Education Department, U.P. (Ex-officio) Near G.P.O., Civil Lines, Allahabad 211 001 9. Shri S. L. Mehta 4, Clive Row, Kolkata 700 001 10. Shri Avnish Mehta 4, Penn Road, Kolkata 700 027 11. Shri Rajnish Mehta 4, Penn Road, Kolkata 700 027 12. Prof. Pinaki Majumdar Director (Ex-Officio) Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 6 Academic Staff Faculty Members (Mathematics) 1. Batra, Punita 2. Chakraborty, Kalyan 3. Dalawat, C.S. 4. Dubey, Umesh Kumar V. 5. Kumar, Manoj 6. Prakash, Gyan 7. Raghavendra, N. 8. Ramakrishnan, B. 9. Ramana, D. Surya 10. Ratnakumar, P. K. 11. Shah, Hemangi M. 12. Thangadurai. R. Faculty Members (Physics) 1. Basu, Anirban 2. Das, Tapas Kumar 3. Datta, AseshKrishna 4. De, Aditi Sen 5. Gandhi, Raj 6. Jatkar, Dileep 7. Maharana, Anshuman 8. Majumdar, Pinaki 9. Pareek, T. P. 10. Pati, Arun Kumar 11. Rai, Santosh Kumar 12. Rao, Sumathi 13. Sen, Ashoke 14. Sen, Prasenjit 15. Sen, Ujjwal 7 Administrative Staff 1. Shri Ravindra Singh [Registrar] 2. Shri Rajkumar Gulati [Accounts Officer] 3. Shri Manish Sharma [S.O.‘E’] 4. Shri K.K. Suresh Kumar [Librarian] 5. Shri Amit Roy [I.A.&A.O.] 6.
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